**1. Introduction**

The combined convective movement and thermal energy transfer have been examined in a huge number of studies for decades because of its applications in numerous fields of technological sciences. Since the communal interaction among the viscous, buoyancy, and inertia forces on the stream has been a vital matter for joint convection in a lid-driven enclosed box, the moving wall's direction of the cavity becomes significant in these studies [1–4]. Therefore, the current work keenly involves the influence of moving-wall direction on convective stream in lid-driven cavities. Combined convection together with heat transfer have been examined under several conditions in enormous studies [5–9]. Sivasankaran et al. [10] numerically explored the mixed convective stream and the energy transport in an inclined enclosed space with discrete heating. Sivasankaran and Pan [11] discovered the influence of discrete heaters and coolers on convection in a closed box. Mekroussi et al. [12] explored the combined convection in a top-driven inclined wavy walled box. Combined convection flow due to nonuniform heating in an enclosed box is discovered in some studies [13–15].

Nanofluids are pioneering fluids in the field of thermal science and it has been used actively to analyze the energy transport in thermal systems [16–22]. Sheremet et al. [21] discovered the buoyant flow and entropy generation of nanoliquid in a closed box with variable border temperature.

Alsabery et al. [22] numerically explored the entropy generation and convection of nanoliquid in a wavy walled box. Santra et al. [23] deliberated the energy transfer augmentation of a water–copper nanoliquid in a di fferentially heated box. Abu-Nada and Oztop [24] discovered the outcome of inclination of the box on convection of a Cu–water nanofluid. Ghasemi and Aminossadati [25] explored the buoyant convection of a CuO nanoliquid in an inclined box numerically. Bhuvaneswari et al. [26] completed a numeric work to ge<sup>t</sup> the impact of variable liquid properties on convective stream of a nanoliquid in a square box. Sivasankaran et al. [27] inspected the partial slip influence on magneto-convection in a 2-sided wall-driven porous enclosed space filled with a Cu–water nanoliquid. Rashad et al. [28] discovered the magneto-convection of heat generating nanoliquids in a trapezoidal box with discrete heating.

The interaction connecting natural/mixed convection and thermal radiation has gained significant consideration due to its uses in various arenas. Very few studies on the interaction of thermal radiation and convective stream have been reported in the literature [29–34]. Mansour et al. [29] discovered the outcome of radiation on buoyant convection in a porous wavy enclosed space using the non-equilibrium thermal model. They found that average heat transport decreased by increasing the surface waviness of the wall. The doubly di ffusive convection with radiation in an enclosed box was explored by Moufekkir et al. [30]. Mahapatra et al. [31] explored the influence of heat generation and thermal radiation on magneto-convective stream in an inclined enclosed space with one hot side and chilled from the adjacent side. They concluded that the direction of the magnetic field influenced much on the stream pattern. Saleem et al. [32] scrutinized the impact of radiation on buoyant convection in an open box. They demonstrated that radiative heat transport increased as the optical thickness of the liquid increased. Zhang et al. [33] explored the e ffects of thermal radiation on magneto-convection in a cavity.

Since no study on combined convection of a nanoliquid in a wall-driven box with thermal radiation and entropy generation is reported in the literature, the current investigation is interested to investigate numerically the e ffect of entropy, thermal radiation and the direction of wall movement of an enclosed box on the convective stream and energy transfer of a nanoliquid.
